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| 1 |
Algebra I Preps |
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| 2 |
Dummit and Foote, Chapters 1-12 |
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| 3 |
Lang, Chapters I-IV |
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| 4 |
Selick's Notes |
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| 5 |
Study |
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| 6 |
Groups of Order pq |
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| 7 |
--- Sylow's Theorem |
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| 8 |
--- Cauchy's Theorem on Abelian Groups |
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| 9 |
Finitely Generated Abelian Groups |
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| 10 |
Modules over PID's |
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| 11 |
--- Modules of a PID - comments |
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| 12 |
--- Using Gaussian Elimination |
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| 13 |
--- Greg's way |
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| 14 |
Noetherian Rings and Modules |
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| 15 |
By-The-Week Plan |
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2010-12-16 17:29:30 |
| 16 |
Conventions for Permutations |
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| 17 |
September 14, hours 1-2 - Non Commutative Gaussian Elimination |
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| 18 |
--- Scratch Page for September 14 |
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| 19 |
September 16, hour 3 - Non Commutative Gaussian Elimination, Homomorphisms, Kernels and Images |
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| 20 |
--- The Isomorphism Theorems, the Butterfly Lemma and Jordan-Holder |
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| 21 |
September 21, hours 4-5: Quotients and The First Isomorphism Theorem |
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| 22 |
September 23, hour 6: Isomorphism Theorems 2-4 |
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| 23 |
September 28, hours 7-8: The Butterfly and Jordan-Holder |
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| 24 |
September 30, hour 9: S_n and A_n |
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| 25 |
October 5, hours 10-11: A_n is Simple, G-Actions |
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| 26 |
October 7, hour 12: G-Actions, Sylow 0 |
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| 27 |
October 12, hours 13-14: The Sylow Theorems |
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| 28 |
October 14, hour 15: The Sylow Theorems, Semi-Direct Products |
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| 29 |
October 19, hours 16-17: Semi-Direct Products, braids |
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| 30 |
October 21, hour 18: Braids, Orders pq and 12, Solvable groups |
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| 31 |
October 26, hours 19-20: Term Test |
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| 32 |
October 28, hour 21: Left and right, Sylow apps, solvability |
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| 33 |
November 2, hours 22-23: Rings |
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| 34 |
November 4, hour 24: Maximal & Prime Ideals |
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| 35 |
--- Lims |
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| 36 |
November 11, hour 25: Prime ideals, primes |
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| 37 |
--- Planning Page for November 11 |
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| 38 |
November 16, hours 26-27: UFDs, Euc->PID->UFD |
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| 39 |
--- Planning Page for November 16 |
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| 40 |
November 18, hour 28: The ring of modules |
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| 41 |
November 23, hours 29-30: Existence part for modules over a PID, justice for tensor products |
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| 42 |
November 25, hour 31: Justice for tensor products, uniqueness part for modules over a PID |
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| 43 |
--- November 25 Scratch |
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| 44 |
November 30, hours 32-33: Uniqueness part for modules over a PID, applications |
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| 45 |
December 2, hour 34: The Jordan Canonical Form |
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| 46 |
--- Cayley-Hamilton |
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| 47 |
December 7, hours 35-36: Unboxing the Jordan Canonical Form |
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| 48 |
--- Boxing Day Handout, 1 |
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| 49 |
--- Boxing Day Handout, 2 |
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| 50 |
--- Boxing Day |
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| 51 |
--- Boxing Day Scratch |
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